B&W 802D1 - How can I tame the brightness?

"B&W sells more speakers, high end speakers, than any other company in the world.  And the 802 D diamond is one of their best, many prefer it to more recent iterations of the 802 series."

I can tell by your post you've never had a pair of these speakers. The reason B&W sells so many speakers is they look nice, have an exciting sound that makes you say "wow" when you first hear them and they have really good distribution. Most high end speaker brands don't have the manufacturing capacity to fill a chain like BestBuy.

If you notice from the comments, most of us had B&W speakers at one time. But the key word is had. So yes, they sell a lot of speakers but people tend not to keep them. 

I know some people mentioned fooling with the room. It won't fix this problem. Unless you are willing to put something in between you and the tweeter, it won't help. And when I say help, I mean cover up, not fix. You can spend a fortune trying to fix these speakers. I'm not saying you can't get them to sound good, its just that it may be more trouble than its worth. If the choice was mine, I would get different speakers and be done with it. 

Tekton Double Impact loudspeakers will blow your musical mind - and leave you with lots of cash to put towards high quality sources.

Because the solution to too-much-brightness is more-brightness.

The best way to fix speakers that are not pleasing to you is to get new speakers. There are so many good ones to choose from that it can be overwhelming. You might  start by auditioning the Sonos Faber Serafinos 

These are excellent speakers with a touch of warmth that will never be fatiguing. Some people might find them “soft” while others will think the presentation is exactly what they want. No substitute for listening.
 

"I can tell by your post you've never had a pair of these speakers."

LOL!  As a matter of fact I do own a pair of these speakers.  I know them intimately and know their strengths and weaknesses.  With these, or for that matter any speakers, "fooling with the room" is everything.  You have admitted your own limitations in your post.  Make no mistake, though, the OP has a room problem, and 802 D diamonds when properly set up are not overly bright or harsh.  

Unfortunately, that brightness is due to the tweeter and to my ears is very tiring.